Götterdämmerung over total least squares

Malissiovas, Georgios; Neitzel, Frank

doi:10.1515/jogs-2016-0003

Cited by 6 publications

(6 citation statements)

References 10 publications

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“…46-47). This is something that has been observed by Malissiovas et al [15], where a relationship has been presented between TLS and the direct least squares solution of the same adjustment problem, while postulating uncorrelated and equally weighted observations.…”

Section: Introductionsupporting

confidence: 56%

Weighted Total Least Squares (WTLS) Solutions for Straight Line Fitting to 3D Point Data

2020

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In this contribution the fitting of a straight line to 3D point data is considered, with Cartesian coordinates xi, yi, zi as observations subject to random errors. A direct solution for the case of equally weighted and uncorrelated coordinate components was already presented almost forty years ago. For more general weighting cases, iterative algorithms, e.g., by means of an iteratively linearized Gauss–Helmert (GH) model, have been proposed in the literature. In this investigation, a new direct solution for the case of pointwise weights is derived. In the terminology of total least squares (TLS), this solution is a direct weighted total least squares (WTLS) approach. For the most general weighting case, considering a full dispersion matrix of the observations that can even be singular to some extent, a new iterative solution based on the ordinary iteration method is developed. The latter is a new iterative WTLS algorithm, since no linearization of the problem by Taylor series is performed at any step. Using a numerical example it is demonstrated how the newly developed WTLS approaches can be applied for 3D straight line fitting considering different weighting cases. The solutions are compared with results from the literature and with those obtained from an iteratively linearized GH model.

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Section: Introductionsupporting

confidence: 56%

Weighted Total Least Squares (WTLS) Solutions for Straight Line Fitting to 3D Point Data

2020

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“…A direct least squares solution for this non-linear adjustment is possible, as presented by Ceplecha (1987). A discussion of this adjustment problem in the context of total least squares adjustment, taking into account more general weighting cases, is provided by Malissiovas et al (2016) and Malissiovas (2019, pp. 78-81, 113-118).…”

Section: Linear Trajectory From Plane Intersectionmentioning

confidence: 99%

A new least squares adjustment approach for the determination of linear meteor trajectories

Margonis

Malissiovas

Neitzel

et al. 2022

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Context. Precise astrometric measurements performed on meteor images are required to derive the dynamical parameters of a mete-oroid. As a consequence, the measurements carried out in this initial step will have a strong impact on the dynamical solution of an orbiting meteoroid. These measurements relate to the position of the meteor defined by the positions of pixels along its path, as well as by their uncertainties. Therefore, the use of all available information is of great importance for the subsequent processing steps. Aims. This paper examines a new geometrical approach for computing the trajectory of a meteor from multi-station observations. The model considers a more general weighting scheme based on existing stochastic information from the measurements, including the geometry between each station and the observed meteor. Methods. We present a novel mathematical model for least squares adjustment of the linear meteor trajectories within the Gauss-Helmert model, which allows the use of stochastic information from the measured direction vectors from multiple stations. Additionally, an extended stochastic model is presented that takes into account the geometric relationship between each station and the observed meteor as a weight component for each group of observations. Results. The solution of the new approach is demonstrated on a synthetic meteor example, with observations generated from multiple stations with differing precision. The geometric configuration of the stations has been chosen in such a way that it creates the necessity to include stochastic information for the observed direction vectors for a realistic solution. The results of the newly developed approach are compared with those from established methods in the literature. Future investigations and optimisations for developing an even more improved meteor trajectory model are being addressed.

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“…As the number of control points is four or more, the least square adjustment [83] method is used to compute the parameters [a, b, c] from the Equation (14).…”

Section: The Rigid-body Orientationmentioning

confidence: 99%

The Quality Assessment of Different Geolocalisation Methods for a Sensor System to Monitor Structural Health of Monumental Objects

Markiewicz

Łapiński

Kot

et al. 2020

Sensors

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Cultural heritage objects are affected by a wide range of factors causing their deterioration and decay over time such as ground deformations, changes in hydrographic conditions, vibrations or excess of moisture, which can cause scratches and cracks formation in the case of historic buildings. The electromagnetic spectroscopy has been widely used for non-destructive structural health monitoring of concrete structures. However, the limitation of this technology is a lack of geolocalisation in the space for multispectral architectural documentation. The aim of this study is to examine different geolocalisation methods in order to determine the position of the sensor system, which will then allow to georeference the results of measurements performed by this device and apply corrections to the sensor response, which is a crucial element required for further data processing related to the object structure and its features. The classical surveying, terrestrial laser scanning (TLS), and Structure-from-Motion (SfM) photogrammetry methods were used in this investigation at three test sites. The methods were reviewed and investigated. The results indicated that TLS technique should be applied for simple structures and plain textures, while the SfM technique should be used for marble-based and other translucent or semi-translucent structures in order to achieve the highest accuracy for geolocalisation of the proposed sensor system.

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Götterdämmerung over total least squares

Cited by 6 publications

References 10 publications

Weighted Total Least Squares (WTLS) Solutions for Straight Line Fitting to 3D Point Data

Weighted Total Least Squares (WTLS) Solutions for Straight Line Fitting to 3D Point Data

A new least squares adjustment approach for the determination of linear meteor trajectories

The Quality Assessment of Different Geolocalisation Methods for a Sensor System to Monitor Structural Health of Monumental Objects

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